Update readme (#3)

* Update model.md

* Update readme

* Try fix install as package error

* Cleanup main.py

Author: DenHvideDvaerg

README.md

@@ -58,7 +58,12 @@ A Snake puzzle solver using mathematical programming.
 
 ## Overview
 
-Snake is a logic puzzle where ...
+Snake is a logic puzzle where you must create a single connected path on a grid according to these rules:
+
+- **Single connected path** - the snake forms one continuous line from start to end cell
+- **No self-touching** - the snake body never touches itself, neither orthogonally nor diagonally
+- **Row and column constraints** - each row/column must have a specific number of filled cells
+  - **Missing constraints variant** - supports puzzles where some row/column constraints are unknown (specified as `None`)
 
 This solver models the puzzle as a **Mixed Integer Programming (MIP)** problem to find solutions.
 
@@ -70,16 +75,164 @@ pip install snake-mip-solver
 
 ## Requirements
 
-- Python >=3.9
+- Python 3.9+
 - Google OR-Tools
 - pytest (for testing)
 
+## Example Puzzles
+
+### 6x6 Easy Puzzle
+
+This 6x6 puzzle demonstrates a straightforward Snake puzzle:
+
+| Puzzle | Solution |
+|--------|----------|
+| <img src="https://github.com/DenHvideDvaerg/snake-mip-solver/raw/main/images/6x6_Easy.png" width="400"> | <img src="https://github.com/DenHvideDvaerg/snake-mip-solver/raw/main/images/6x6_Easy_solution.png" width="400"> |
+
+```python
+def example_6x6_easy():
+    """6x6 easy example"""
+    puzzle = SnakePuzzle(
+        row_sums=[1, 1, 1, 3, 2, 5],
+        col_sums=[4, 3, 1, 1, 1, 3],
+        start_cell=(0, 0),
+        end_cell=(3, 5)
+    )
+    return puzzle
+```
+
+### 12x12 Evil Puzzle with Missing Constraints
+
+This 12x12 puzzle demonstrates a challenging large-scale puzzle with missing row/column constraints:
+
+| Puzzle | Solution |
+|--------|----------|
+| <img src="https://github.com/DenHvideDvaerg/snake-mip-solver/raw/main/images/12x12_Evil.png" width="400"> | <img src="https://github.com/DenHvideDvaerg/snake-mip-solver/raw/main/images/12x12_Evil_solution.png" width="400"> |
+
+```python
+def example_12x12_evil():
+    """12x12 'Evil' puzzle from https://gridpuzzle.com/snake/evil-12"""
+    puzzle = SnakePuzzle(
+        row_sums=[11, 2, 7, 4, 4, None, None, None, 3, 2, None, 5],
+        col_sums=[9, 7, None, 2, 5, 6, None, None, 5, None, None, None],
+        start_cell=(2, 6),
+        end_cell=(7, 5)
+    )
+    return puzzle
+```
+
 ## Usage
 
 ```python
 from snake_mip_solver import SnakePuzzle, SnakeSolver
+import time
+
+def solve_puzzle(puzzle, name):
+    """Solve a snake puzzle and display results"""
+    print(f"\n" + "="*60)
+    print(f"SOLVING {name.upper()}")
+    print("="*60)
+    
+    # Create and use the solver
+    solver = SnakeSolver(puzzle)
+    
+    print("Solver information:")
+    info = solver.get_solver_info()
+    for key, value in info.items():
+        print(f"  {key}: {value}")
+    
+    print("\nSolving...")
+    start_time = time.time()
+    solution = solver.solve(verbose=False)
+    solve_time = time.time() - start_time
+    
+    if solution:
+        print(f"\nSolution found in {solve_time:.3f} seconds!")
+        print(f"Solution has {len(solution)} filled cells")
+        print(f"Solution: {sorted(list(solution))}")
+        
+        # Display the board with solution
+        print("\nPuzzle with solution:")
+        print(puzzle.get_board_visualization(solution, show_indices=False))
+        
+        # Validate solution
+        if puzzle.is_valid_solution(solution):
+            print("✅ Solution is valid!")
+        else:
+            print("❌ Solution validation failed!")
+    else:
+        print(f"\nNo solution found (took {solve_time:.3f} seconds)")
+
+# Load and solve example puzzles
+puzzle_6x6 = example_6x6_easy()
+solve_puzzle(puzzle_6x6, "6x6 Easy")
+
+puzzle_12x12 = example_12x12_evil()
+solve_puzzle(puzzle_12x12, "12x12 Evil")
+```
 
-# TODO: Make example either a direct copy of or very similar to main.py 
+### Output
+
+```
+============================================================
+SOLVING 6X6 EASY
+============================================================
+Solver information:
+  solver_type: SCIP 9.2.2 [LP solver: SoPlex 7.1.3]
+  num_variables: 36
+  num_constraints: 159
+  puzzle_size: 6x6
+  start_cell: (0, 0)
+  end_cell: (3, 5)
+
+Solving...
+
+Solution found in 0.002 seconds!
+Solution has 13 filled cells
+Solution: [(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (3, 5), (4, 1), (4, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5)]
+
+Puzzle with solution:
+  4 3 1 1 1 3
+1 S _ _ _ _ _
+1 x _ _ _ _ _
+1 x _ _ _ _ _
+3 x x _ _ _ E
+2 _ x _ _ _ x
+5 _ x x x x x
+✅ Solution is valid!
+
+============================================================
+SOLVING 12X12 EVIL
+============================================================
+Solver information:
+  solver_type: SCIP 9.2.2 [LP solver: SoPlex 7.1.3]
+  num_variables: 144
+  num_constraints: 665
+  puzzle_size: 12x12
+  start_cell: (2, 6)
+  end_cell: (7, 5)
+
+Solving...
+
+Solution found in 0.255 seconds!
+Solution has 49 filled cells
+Solution: [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (0, 10), (0, 11), (1, 1), (1, 11), (2, 0), (2, 1), (2, 6), (2, 8), (2, 9), (2, 10), (2, 11), (3, 0), (3, 5), (3, 6), (3, 8), (4, 0), (4, 1), (4, 5), (4, 8), (5, 1), (5, 5), (5, 6), (5, 7), (5, 8), (6, 0), (6, 1), (7, 0), (7, 5), (8, 0), (8, 4), (8, 5), (9, 0), (9, 4), (10, 0), (10, 4), (11, 0), (11, 1), (11, 2), (11, 3), (11, 4)]
+
+Puzzle with solution:
+   9 7 ? 2 5 6 ? ? 5 ? ? ?
+11 _ x x x x x x x x x x x
+ 2 _ x _ _ _ _ _ _ _ _ _ x
+ 7 x x _ _ _ _ S _ x x x x
+ 4 x _ _ _ _ x x _ x _ _ _
+ 4 x x _ _ _ x _ _ x _ _ _
+ ? _ x _ _ _ x x x x _ _ _
+ ? x x _ _ _ _ _ _ _ _ _ _
+ ? x _ _ _ _ E _ _ _ _ _ _
+ 3 x _ _ _ x x _ _ _ _ _ _
+ 2 x _ _ _ x _ _ _ _ _ _ _
+ ? x _ _ _ x _ _ _ _ _ _ _
+ 5 x x x x x _ _ _ _ _ _ _
+✅ Solution is valid!
 ```
 
 ### Running the example
@@ -103,8 +256,15 @@ pytest --cov=snake_mip_solver # Run with coverage
 
 The solver uses **Mixed Integer Programming (MIP)** to model the puzzle constraints. Google OR-Tools provides the optimization framework, with SCIP as the default solver.
 
-See the complete formulation in **[Complete Mathematical Model Documentation](https://github.com/DenHvideDvaerg/snake-mip-solver/blob/main/model.md)**
+The mathematical formulation includes six types of constraints:
+1. **Start and End Cell Constraints** - fixing the path endpoints
+2. **Row Sum Constraints** - ensuring correct number of cells per row
+3. **Column Sum Constraints** - ensuring correct number of cells per column  
+4. **Snake Path Connectivity Constraints** - forming a single connected path
+5. **Diagonal Non-Touching Constraints** - preventing diagonal self-contact
+6. **No 2×2 Block Constraints** - preventing disconnected filled blocks
 
+See the complete formulation in **[Complete Mathematical Model Documentation](https://github.com/DenHvideDvaerg/snake-mip-solver/blob/main/model.md)**
 
 ## License
 

images/12x12_Evil.png

@@ -13,17 +13,6 @@ def example_3x3():
     return puzzle
 
 
-def example_8x8():
-    """8x8 example from https://puzzlegenius.org/snake/"""
-    puzzle = SnakePuzzle(
-        row_sums=[4, 2, 2, 3, 1, 3, 2, 6],
-        col_sums=[3, 2, 7, 2, 2, 4, 1, 2],
-        start_cell=(2, 5),
-        end_cell=(6, 7)
-    )
-    return puzzle
-
-
 def example_diagonal_touching():
     """Diagonal touching example (infeasible)"""
     puzzle = SnakePuzzle(
@@ -44,6 +33,16 @@ def example_adjacent_touching():
     )
     return puzzle
 
+def example_6x6_easy():
+    """6x6 easy example"""
+    puzzle = SnakePuzzle(
+        row_sums=[1, 1, 1, 3, 2, 5],
+        col_sums=[4, 3, 1, 1, 1, 3],
+        start_cell=(0, 0),
+        end_cell=(3, 5)
+    )
+    return puzzle
+
 def example_12x12_evil():
     """12x12 'Evil' puzzle from https://gridpuzzle.com/snake/evil-12"""
     puzzle = SnakePuzzle(
@@ -80,7 +79,7 @@ def solve_puzzle(puzzle, name):
 
         # Display the board with solution
         print("\nPuzzle with solution:")
-        print(puzzle.get_board_visualization(solution, show_indices=True))
+        print(puzzle.get_board_visualization(solution, show_indices=False))
 
         # Validate solution
         if puzzle.is_valid_solution(solution):
@@ -93,17 +92,8 @@ def solve_puzzle(puzzle, name):
 
 def main():
     # Solve different puzzle examples
-    puzzle_3x3 = example_3x3()
-    solve_puzzle(puzzle_3x3, "3x3 Simple")
-
-    puzzle_diag = example_diagonal_touching()
-    solve_puzzle(puzzle_diag, "5x5 Diagonal Touching")
-
-    puzzle_adjacent_touching = example_adjacent_touching()
-    solve_puzzle(puzzle_adjacent_touching, "4x4 Adjacent Touching")
-
-    puzzle_8x8 = example_8x8()
-    solve_puzzle(puzzle_8x8, "8x8")
+    puzzle_6x6 = example_6x6_easy()
+    solve_puzzle(puzzle_6x6, "6x6 Easy")
 
     puzzle_12x12 = example_12x12_evil()
     solve_puzzle(puzzle_12x12, "12x12 Evil")